An EPR-based self-learning approach to material modelling

Keywords: Self-learning Finite element Evolutionary computation Material modelling EPR a b s t r a c t In this paper an EPR-based self-learning method is presented for modelling the constitutive behaviour of materials using evolutionary polynomial regression (EPR). The proposed approach takes advantage of the rich stress–strain data buried in non-homogenous structural tests. The load–deformation data collected from experiment are used to iteratively train EPR-based material model using finite element simulations of the structural test. Two numerical examples are presented to illustrate the application of the proposed approach. It is shown that the EPR model gradually improves during the self-learning training and provides accurate prediction for the constitutive behaviour of the material. Evolutionary polynomial regression (EPR) is a new hybrid technique for creating true or pseudo-polynomial models from observed data by integrating the power of least square regression with the efficiency of genetic algorithm (GA) [1]. EPR is proven to be capable of learning complex non-linear relationships from a large set of data, and it has many desirable features for engineering applications. The EPR technique has been successfully applied to modelling a wide range of complex engineering problems including stability of slopes [2]; liquefaction of soils [3]; mechanical behaviour of rubber concrete [4], torsional strength of reinforced concrete beams [5] and many other applications in Civil and Mechanical engineering. The use of EPR to develop material consti-tutive models (as an alternative to conventional material modelling) has also been proposed by the authors and their co-workers [6–10]. When using EPR for material modelling, the raw experimental or in situ data are directly used for training the EPR model. Since the EPR learns the constitutive relationships directly from raw data, it is the shortest route from experimental research to numerical modelling. In this approach there are no material parameters to be identified and as more data become available, the model can be improved by retraining of the EPR using the additional data. Furthermore, the incorporation of an EPR model in finite element procedure avoids the need for complex yield/failure functions , flow rules, etc. An EPR model can be incorporated in a finite element code/procedure in the same way as a conventional constitutive model. The training of EPR material models that has been described in previous works [6–10] is a straightforward approach in which a set of experimentally measured stress–strain data has been used to develop the EPR-based material model. However one …